Zermatt is one of the cutest little ski resort villages that you could imagine and the locals take steps to keep it that way so much so that little has changed since my previous visit over 30 years ago.
Although, by and large, only electric vehicles are permitted in the village, it isn't a pedestrian zone so keep an eye out when you're crossing the road. Avoid going during May as that's when construction vehicles are permitted into the town.
Most people leave their car at Tasch where you have the choice of covered parking at around SF 13 per day or open air parking at half that. Some hotels and other establishments in Tasch will let you leave your car with them during your stay in Zermatt.
The train from Tasch runs every 20 minutes to Zermatt and it doesn't take long before you are pulling into the station which is pretty much in the centre of the village. The first shop you'll come to is the small newsagent which rather unhelpfully doesn't take credit/debit cards despite the untold numbers that she's obviously been offered.
Although you can arrive directly in Zermatt and book accommodation there, it's best to check availability whilst you're in the station in Tasch. Most hotels stay open only during the main seasons so if you're arriving in, say, October/November you will find a lot of them closed.
If you're there for the ski-ing, you'll be spoilt for choice in terms of numbers and skill-levels of the slopes. This is quite a high altitude resort so the season is relatively long. Those who've not bought their clothing or equipment in advance will find numerous shops that are able to help you but so watch the prices.
To see the view that is probably most representative of Switzerland ie the Matterhorn you can go to Gornergrat via the mountain railway which gives some spectacular views along its ascent (sit on the right going up to see the Matterhorn). It's possible to stay in the hotel at Gornergrat and there is a very small shopping centre and a couple of restaurants. As an alternative to this, you can get a similar view by taking one of the cable cars up to Matterhorn or Schwarzsee paradise which both give a more spectacular if much more expensive experience.
There isn't a whole lot to see in Zermatt itself but don't miss the small church where you'll find the graves of numerous climbers from years gone by. There's a new Matterhorn museum just beside the church.
The nearest airport is Geneva (GVA) which is served by a surprisingly small number of airlines given the reputation of the city.
You can reach Tasch via the train from Visp which connects to services to Geneva etc. The train to Gornergrat is quite expensive at over SF 70 return (children under 6 are free).